make a wired remote control for a toy car

The simplest and cheapest way to do it is with off the shelf Radio Control (for models). Any hobby shop. If this is an exercise, it is a matter of how complicated you want.

At the simple end push buttons in the control operate relays in the car which switch the motors. This can be done with logic circuits (flip flops as latches) and power transistors or power FETs as switches too.. You could use potentiometers to set the position of servo motors fo steering. These servo motors have position feedback.

If you want some kind of proportional/position control the best idea is to use RC servos in the car (say for steering). These are position servos that move to an angle depending on the width of a control pulse. You have to generate variable width pulses of the right proportions. Look up how they work, and you will see that quite a simple circuit can do this job for one channel. Think of a pair of opamps or 555 timers. Several can be controlled by using separate wires, or by assembling (multiplexing) the pulses into a pulse train as is done with radio control. It is disassembled at the car end. This needs suitable electronics. Maybe you could hack into cheap radio control units, bypas the transmitter and receiver basically, with wires.

Another method is to have a microcontroller (such as the Basic Stamp, Arduino, PicAxe) in the car. A PC or other computer sends commands (text messages) over the cable using a serial port (RS232). The computer in the car can be programmed to operate relays, or generate those pulses to control RC servos, etc. This is the most flexible, as it could also reply to commands, even send readings back. Probably the most effort if you are starting ffrom scratch, but also the most rewarding for your career.. You can find software examples for most of this on the net, look up PIC (microcontrollers) with the software you want, e.g. stepper motor, RC servo, serial port.